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Comprehensive Trigonometry Review: Radians, Special Angles, and Graphs

This review covers essential trigonometry concepts including radians and their conversion to and from degrees. Explore special angles and their corresponding coordinates on the unit circle, along with definitions of trigonometric functions and their signs across different quadrants. Dive into graphing fundamental trigonometric functions like sine and cosine, examining period, amplitude, phase shifts, and graph transformations. Learn important trigonometric identities and strategies for solving equations using algebra and inverse functions to fully master the subject.

sigourney-wiley
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Comprehensive Trigonometry Review: Radians, Special Angles, and Graphs

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  1. Trigonometry Review

  2. radians, so radians To convert from degrees to radians, multiply by To convert from radians to degrees, multiply by Angle Measurement

  3. r=1 Special Angles

  4. π/2 π/3 3π/4 2π/3 π/4 5π/6 π/6 π 0 3π/2 r=1 Special Angles - Unit Circle Coordinates

  5. r (x,y)  Trig Functions - Definitions

  6. hyp opp  adj Trig Functions - Definitions

  7. Trig Functions - Definitions

  8. Trig Functions Signs by quadrants sin, csc positive all functions positive tan, cot positive cos, sec positive

  9. example: Special Angles - Triangles

  10. Special Angles - Triangles

  11. r=1 Special Angles - Unit Circle

  12. (0,1) r = 1 (-1,0) (1,0) (0,-1) Use the unit circle points (1,0), (0,1), (-1,0) and (0,-1) or look at the graphs for the trig functions example: Special Angles For the angles

  13. y = sin x 1 -π/2 π/2 π 3π/2 2π -1 Period is and amplitude is 1. Graphing Trigonometry Functions Basic Graphs

  14. y = cos x 1 -π/2 π/2 π 3π/2 2π -1 Period is and amplitude is 1. Graphing Trigonometry Functions Basic Graphs

  15. Using the graph for Special Angles and Graphs

  16. y = a sin x a -π/2 π/2 π 3π/2 2π -a Period is and amplitude is a. Graphing Trig Functions Amplitude Change y= a sin x stretches or compresses the graph vertically

  17. y = sin(x -b) 1 b 2π+b -1 Period is and amplitude is 1. Graphing Trig Functions Phase Shift y = sin(x -b) slides graph right by bunits

  18. y = sin(x +b) 1 -1 -b 2π -b Period is and amplitude is 1. Graphing Trig Functions Phase Shift y = sin(x + b) slides graph left by bunits

  19. 1 2π/c -1 Period is and amplitude is 1. Graphing Trig Functions Period Change y = sin cx stretches or compresses the graph horizontally

  20. Trig Identities Reciprocal Quotient

  21. Trig Identities Pythagorean

  22. Trig Identities Double Angle

  23. TrigIdentities Sum and difference

  24. is equivalent to is equivalent to Inverse Trig Functions

  25. example: if and since in quadrants I and II Solving Trig Equations Use algebra, then inverse trig functions or knowledge of special angles to solve.

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